Participant selects political party affiliation which then becomes the political party of the majority group.
Majority group opinions deviate away from participant’s choice on 8 issues with possible condition randomly selected (deviation threshold = [0/25/50/75/100%]).
Hypothesis:Method: 8 issues, 8 agents; deviance is across agents within each issue (deviance not linked to specific agent; deviant agents randomized within each issue)
On trial 1: “On the screens that follow you’re going to learn about a collection of people we polled on a series of political issues. Like yourself, they also most identify with the Independent party. You are going to make guesses about and receive feedback on their positions on a series of 8 political issues. You don’t have to remember what each person’s position is, but try to see if you can figure out to what extent each person agrees with everyone else.”
| 0 (N=60) |
0.25 (N=58) |
0.5 (N=56) |
0.75 (N=67) |
1 (N=68) |
Overall (N=309) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 38.7 (12.6) | 41.9 (12.2) | 36.8 (14.4) | 37.2 (13.0) | 37.2 (13.0) | 38.3 (13.1) |
| Median [Min, Max] | 36.5 [18.0, 69.0] | 39.0 [21.0, 68.0] | 32.5 [18.0, 72.0] | 34.0 [18.0, 73.0] | 34.0 [18.0, 72.0] | 35.0 [18.0, 73.0] |
| race | ||||||
| American Indian or Alaska Native | 1 (1.7%) | 0 (0%) | 2 (3.6%) | 4 (6.0%) | 1 (1.5%) | 8 (2.6%) |
| Asian | 5 (8.3%) | 4 (6.9%) | 6 (10.7%) | 6 (9.0%) | 4 (5.9%) | 25 (8.1%) |
| Black or African-American | 4 (6.7%) | 3 (5.2%) | 4 (7.1%) | 6 (9.0%) | 5 (7.4%) | 22 (7.1%) |
| Hispanic/Latinx | 1 (1.7%) | 4 (6.9%) | 3 (5.4%) | 3 (4.5%) | 6 (8.8%) | 17 (5.5%) |
| White | 49 (81.7%) | 46 (79.3%) | 40 (71.4%) | 48 (71.6%) | 51 (75.0%) | 234 (75.7%) |
| Other | 0 (0%) | 1 (1.7%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (0.3%) |
| Native Hawaiian or Other Pacific Islander | 0 (0%) | 0 (0%) | 1 (1.8%) | 0 (0%) | 1 (1.5%) | 2 (0.6%) |
| gender | ||||||
| Another gender not listed here | 2 (3.3%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (0.6%) |
| Man | 22 (36.7%) | 23 (39.7%) | 23 (41.1%) | 28 (41.8%) | 39 (57.4%) | 135 (43.7%) |
| Woman | 36 (60.0%) | 34 (58.6%) | 30 (53.6%) | 38 (56.7%) | 26 (38.2%) | 164 (53.1%) |
| Non-binary | 0 (0%) | 1 (1.7%) | 3 (5.4%) | 1 (1.5%) | 1 (1.5%) | 6 (1.9%) |
| Prefer not to answer | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (2.9%) | 2 (0.6%) |
| polparty | ||||||
| Democratic | 26 (43.3%) | 28 (48.3%) | 31 (55.4%) | 34 (50.7%) | 36 (52.9%) | 155 (50.2%) |
| Independent | 21 (35.0%) | 16 (27.6%) | 17 (30.4%) | 17 (25.4%) | 23 (33.8%) | 94 (30.4%) |
| Republican | 13 (21.7%) | 14 (24.1%) | 8 (14.3%) | 16 (23.9%) | 9 (13.2%) | 60 (19.4%) |
| 0 (N=8) |
0.25 (N=4) |
0.5 (N=12) |
0.75 (N=5) |
1 (N=7) |
Overall (N=36) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 44.8 (12.0) | 45.3 (8.22) | 36.3 (11.5) | 47.0 (19.1) | 32.7 (10.3) | 40.0 (12.9) |
| Median [Min, Max] | 47.0 [23.0, 59.0] | 45.5 [36.0, 54.0] | 34.0 [19.0, 53.0] | 46.0 [19.0, 70.0] | 35.0 [19.0, 45.0] | 40.5 [19.0, 70.0] |
| race | ||||||
| Hispanic/Latinx | 1 (12.5%) | 0 (0%) | 1 (8.3%) | 0 (0%) | 1 (14.3%) | 3 (8.3%) |
| White | 7 (87.5%) | 4 (100%) | 7 (58.3%) | 4 (80.0%) | 4 (57.1%) | 26 (72.2%) |
| Asian | 0 (0%) | 0 (0%) | 1 (8.3%) | 0 (0%) | 1 (14.3%) | 2 (5.6%) |
| Black or African-American | 0 (0%) | 0 (0%) | 2 (16.7%) | 1 (20.0%) | 1 (14.3%) | 4 (11.1%) |
| Other | 0 (0%) | 0 (0%) | 1 (8.3%) | 0 (0%) | 0 (0%) | 1 (2.8%) |
| gender | ||||||
| Man | 5 (62.5%) | 2 (50.0%) | 7 (58.3%) | 1 (20.0%) | 1 (14.3%) | 16 (44.4%) |
| Woman | 3 (37.5%) | 2 (50.0%) | 5 (41.7%) | 4 (80.0%) | 6 (85.7%) | 20 (55.6%) |
| polparty | ||||||
| Democratic | 3 (37.5%) | 2 (50.0%) | 5 (41.7%) | 3 (60.0%) | 3 (42.9%) | 16 (44.4%) |
| Independent | 3 (37.5%) | 2 (50.0%) | 5 (41.7%) | 2 (40.0%) | 2 (28.6%) | 14 (38.9%) |
| Republican | 2 (25.0%) | 0 (0%) | 2 (16.7%) | 0 (0%) | 2 (28.6%) | 6 (16.7%) |
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: corrresp
Chisq Df Pr(>Chisq)
opinion_round 79.75 1 < 2.2e-16 ***
Deviant_threshold 1128.01 4 < 2.2e-16 ***
opinion_round:Deviant_threshold 160.68 4 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 1 opinion_round.trend SE df asymp.LCL asymp.UCL z.ratio p.value
overall 0.146 0.0112 Inf 0.124 0.168 13.013 <.0001
Results are averaged over the levels of: Deviant_threshold
Confidence level used: 0.95 $emmeans
Deviant_threshold emmean SE df asymp.LCL asymp.UCL z.ratio p.value
0 3.2244 0.1053 Inf 3.018 3.4308 30.628 <.0001
0.25 0.4774 0.0652 Inf 0.350 0.6052 7.322 <.0001
0.5 -0.0305 0.0658 Inf -0.159 0.0985 -0.463 0.6433
0.75 -0.0892 0.0604 Inf -0.208 0.0293 -1.476 0.1401
1 2.0746 0.0759 Inf 1.926 2.2232 27.349 <.0001
Results are given on the logit (not the response) scale.
Confidence level used: 0.95
$contrasts
contrast estimate SE df asymp.LCL
Deviant_threshold0 - Deviant_threshold0.25 2.7470 0.1228 Inf 2.412
Deviant_threshold0 - Deviant_threshold0.5 3.2549 0.1233 Inf 2.919
Deviant_threshold0 - Deviant_threshold0.75 3.3136 0.1205 Inf 2.985
Deviant_threshold0 - Deviant_threshold1 1.1499 0.1259 Inf 0.807
Deviant_threshold0.25 - Deviant_threshold0.5 0.5079 0.0915 Inf 0.258
Deviant_threshold0.25 - Deviant_threshold0.75 0.5666 0.0877 Inf 0.327
Deviant_threshold0.25 - Deviant_threshold1 -1.5972 0.0987 Inf -1.867
Deviant_threshold0.5 - Deviant_threshold0.75 0.0587 0.0881 Inf -0.182
Deviant_threshold0.5 - Deviant_threshold1 -2.1050 0.0993 Inf -2.376
Deviant_threshold0.75 - Deviant_threshold1 -2.1637 0.0959 Inf -2.425
asymp.UCL z.ratio p.value
3.082 22.374 <.0001
3.591 26.404 <.0001
3.642 27.490 <.0001
1.493 9.136 <.0001
0.757 5.552 <.0001
0.806 6.463 <.0001
-1.328 -16.175 <.0001
0.299 0.666 0.9636
-1.834 -21.191 <.0001
-1.902 -22.560 <.0001
Results are given on the log odds ratio (not the response) scale.
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates $emtrends
Deviant_threshold opinion_round.trend SE df asymp.LCL asymp.UCL z.ratio
0 0.3096 0.0380 Inf 0.23515 0.3841 8.149
0.25 0.0298 0.0182 Inf -0.00581 0.0653 1.640
0.5 0.0316 0.0181 Inf -0.00393 0.0672 1.743
0.75 0.0225 0.0167 Inf -0.01016 0.0551 1.350
1 0.3353 0.0250 Inf 0.28628 0.3844 13.397
p.value
<.0001
0.1010
0.0813
0.1770
<.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df asymp.LCL
Deviant_threshold0 - Deviant_threshold0.25 0.27985 0.0420 Inf 0.1652
Deviant_threshold0 - Deviant_threshold0.5 0.27800 0.0421 Inf 0.1632
Deviant_threshold0 - Deviant_threshold0.75 0.28713 0.0415 Inf 0.1739
Deviant_threshold0 - Deviant_threshold1 -0.02573 0.0442 Inf -0.1463
Deviant_threshold0.25 - Deviant_threshold0.5 -0.00185 0.0257 Inf -0.0718
Deviant_threshold0.25 - Deviant_threshold0.75 0.00728 0.0246 Inf -0.0599
Deviant_threshold0.25 - Deviant_threshold1 -0.30557 0.0308 Inf -0.3896
Deviant_threshold0.5 - Deviant_threshold0.75 0.00913 0.0246 Inf -0.0580
Deviant_threshold0.5 - Deviant_threshold1 -0.30372 0.0309 Inf -0.3880
Deviant_threshold0.75 - Deviant_threshold1 -0.31286 0.0301 Inf -0.3949
asymp.UCL z.ratio p.value
0.3945 6.660 <.0001
0.3928 6.603 <.0001
0.4003 6.919 <.0001
0.0948 -0.582 0.9777
0.0681 -0.072 1.0000
0.0745 0.296 0.9983
-0.2216 -9.922 <.0001
0.0763 0.371 0.9960
-0.2194 -9.828 <.0001
-0.2308 -10.401 <.0001
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
targetpair 6285 6285 1 309 23.131 2.368e-06 ***
Deviant_threshold 45899 45899 1 309 168.934 < 2.2e-16 ***
targetpair:Deviant_threshold 69626 69626 1 309 256.261 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emtrends
targetpair Deviant_threshold.trend SE df lower.CL upper.CL t.ratio p.value
PS -62.37 2.65 309 -67.59 -57.15 -23.514 <.0001
SS 1.24 3.45 309 -5.55 8.03 0.359 0.7198
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio p.value
PS - SS -63.6 3.97 309 -71.4 -55.8 -16.008 <.0001
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95 Analysis of Variance Table
Response: k
Df Sum Sq Mean Sq F value Pr(>F)
Deviant_threshold 4 35.897 8.9742 13.891 2.045e-10 ***
Residuals 303 195.758 0.6461
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
Deviant_threshold emmean SE df lower.CL upper.CL t.ratio p.value
0 1.38 0.1038 303 1.18 1.59 13.329 <.0001
0.25 1.37 0.1055 303 1.16 1.57 12.940 <.0001
0.5 1.56 0.1074 303 1.35 1.77 14.511 <.0001
0.75 1.99 0.0982 303 1.79 2.18 20.235 <.0001
1 2.20 0.0982 303 2.01 2.40 22.425 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL
Deviant_threshold0 - Deviant_threshold0.25 0.0174 0.148 303 -0.389
Deviant_threshold0 - Deviant_threshold0.5 -0.1755 0.149 303 -0.585
Deviant_threshold0 - Deviant_threshold0.75 -0.6039 0.143 303 -0.996
Deviant_threshold0 - Deviant_threshold1 -0.8190 0.143 303 -1.211
Deviant_threshold0.25 - Deviant_threshold0.5 -0.1929 0.151 303 -0.606
Deviant_threshold0.25 - Deviant_threshold0.75 -0.6213 0.144 303 -1.017
Deviant_threshold0.25 - Deviant_threshold1 -0.8364 0.144 303 -1.232
Deviant_threshold0.5 - Deviant_threshold0.75 -0.4284 0.146 303 -0.828
Deviant_threshold0.5 - Deviant_threshold1 -0.6435 0.146 303 -1.043
Deviant_threshold0.75 - Deviant_threshold1 -0.2151 0.139 303 -0.596
upper.CL t.ratio p.value
0.424 0.117 1.0000
0.234 -1.175 0.7654
-0.212 -4.227 0.0003
-0.427 -5.733 <.0001
0.220 -1.281 0.7030
-0.226 -4.310 0.0002
-0.441 -5.802 <.0001
-0.029 -2.944 0.0286
-0.244 -4.421 0.0001
0.166 -1.549 0.5316
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Deviant_threshold emmean SE df null t.ratio p.value
0 1.38 0.1038 303 2 -5.945 <.0001
0.25 1.37 0.1055 303 2 -6.010 <.0001
0.5 1.56 0.1074 303 2 -4.109 <.0001
0.75 1.99 0.0982 303 2 -0.132 0.4475
1 2.20 0.0982 303 2 2.058 0.9798
P values are left-tailed # A tibble: 2 × 13
model term estimate std.error statistic p.value conf.low
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 below_.5 Deviant_threshold -41.1 9.39 -4.37 0.0000211 -59.6
2 above_.5 Deviant_threshold 45.6 9.45 4.82 0.00000293 26.9
conf.high r.squared adj.r.squared df df.residual nobs
<dbl> <dbl> <dbl> <dbl> <int> <int>
1 -22.5 0.100 0.0948 1 172 174
2 64.2 0.110 0.105 1 189 191Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 32920 8230 12.88 1.066e-09 ***
Residuals 304 194249 639
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
deviance emmean SE df lower.CL upper.CL t.ratio p.value
0 59.3 3.26 304 52.9 65.8 18.182 <.0001
0.25 43.0 3.32 304 36.5 49.5 12.950 <.0001
0.5 38.9 3.38 304 32.3 45.6 11.530 <.0001
0.75 37.1 3.09 304 31.0 43.2 12.020 <.0001
1 60.9 3.07 304 54.8 66.9 19.852 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio
deviance0 - deviance0.25 16.35 4.65 304 3.58 29.12 3.513
deviance0 - deviance0.5 20.39 4.70 304 7.50 33.28 4.341
deviance0 - deviance0.75 22.21 4.49 304 9.88 34.54 4.944
deviance0 - deviance1 -1.52 4.48 304 -13.81 10.77 -0.339
deviance0.25 - deviance0.5 4.04 4.74 304 -8.96 17.03 0.852
deviance0.25 - deviance0.75 5.86 4.53 304 -6.58 18.30 1.293
deviance0.25 - deviance1 -17.87 4.52 304 -30.27 -5.47 -3.955
deviance0.5 - deviance0.75 1.83 4.58 304 -10.73 14.39 0.399
deviance0.5 - deviance1 -21.91 4.56 304 -34.42 -9.39 -4.803
deviance0.75 - deviance1 -23.73 4.35 304 -35.67 -11.79 -5.454
p.value
0.0046
0.0002
<.0001
0.9971
0.9138
0.6956
0.0009
0.9946
<.0001
<.0001
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates | 0 (N=60) |
0.25 (N=58) |
0.5 (N=56) |
0.75 (N=67) |
1 (N=68) |
Overall (N=309) |
|
|---|---|---|---|---|---|---|
| pred_par | ||||||
| Yes | 54 (90.0%) | 48 (82.8%) | 37 (66.1%) | 32 (47.8%) | 14 (20.6%) | 185 (59.9%) |
| No | 6 (10.0%) | 10 (17.2%) | 19 (33.9%) | 35 (52.2%) | 54 (79.4%) | 124 (40.1%) |
# A tibble: 4 × 14
# Groups: pred_par [2]
pred_par id term estimate std.error statistic p.value
<lgl> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 FALSE below_.5 Deviant_threshold -19.6 19.0 -1.03 0.309
2 FALSE above_.5 Deviant_threshold 78.0 12.3 6.35 0.00000000555
3 TRUE below_.5 Deviant_threshold -41.6 11.0 -3.77 0.000241
4 TRUE above_.5 Deviant_threshold -15.8 15.1 -1.05 0.298
conf.low conf.high r.squared adj.r.squared df df.residual nobs
<dbl> <dbl> <dbl> <dbl> <dbl> <int> <int>
1 -58.3 19.1 0.0313 0.00193 1 33 35
2 53.6 102. 0.275 0.269 1 106 108
3 -63.5 -19.8 0.0940 0.0874 1 137 139
4 -45.9 14.3 0.0134 0.00119 1 81 83Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 32920 8230.0 13.7765 2.526e-10 ***
pred_par 1 682 681.5 1.1408 0.2863
deviance:pred_par 4 14947 3736.8 6.2553 7.596e-05 ***
Residuals 299 178620 597.4
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Analysis of Variance Table
Response: groupid
Df Sum Sq Mean Sq F value Pr(>F)
Deviant_threshold 1 139479 139479 298.4 < 2.2e-16 ***
Residuals 307 143500 467
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 1 Deviant_threshold.trend SE df lower.CL upper.CL t.ratio p.value
overall -59.3 3.43 307 -66 -52.5 -17.274 <.0001
Confidence level used: 0.95 Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Deviant_threshold 497.74 124.43 4 309 1.2459 0.29145
time 1587.61 1587.61 1 309 15.8958 8.358e-05 ***
Deviant_threshold:time 936.42 234.10 4 309 2.3439 0.05478 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
time emmean SE df lower.CL upper.CL t.ratio p.value
before 67.6 1.5 357 64.7 70.6 45.034 <.0001
after 64.4 1.5 357 61.4 67.4 42.892 <.0001
Results are averaged over the levels of: Deviant_threshold
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio p.value
before - after 3.22 0.806 309 1.63 4.8 3.987 0.0001
Results are averaged over the levels of: Deviant_threshold
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95 Similarity Analysis, doesn’t make sense to compare “deviant” vs “nondeviant” learning in this design where deviance is spread across agents (there is no specific deviant).
On the prediction of the new agent’s choice based on the last opinion, the moderator here is whether participants chose the same respond they themselves did.